One of the most challenging experiences in photography is taking images in low-light environments. The basic principle of photography is the accumulation of photons in the sensor during a given exposure time. In general, the more photons reach the surface of the sensor the better quality of the final image, as the photonic noise is reduced. However, this basic principle requires the photographed scene to be static and that there is no relative motion between the camera and the scene. Otherwise, the photons will be accumulated in neighboring pixels, generating a loss of sharpness (blur). This problem is significant when shooting with hand-held cameras, the most popular photography device today, in dim light conditions.
Under reasonable hypothesis, the camera shake may be modeled mathematically as a convolution,v=u★k+n,  (1)Where, v is the noisy blurred observation, μ is the latent sharp image, κ is an unknown blurring kernel and η is additive white noise. For this model to be accurate, the camera movement has to be essentially a rotation with negligible in-plane rotation in its optical axis. The kernel, κ, results from several blur sources: light diffraction due to the finite aperture, out-of-focus, light integration in the photo-sensor, and relative motion between the camera and the scene during the exposure. To get enough photons per pixel in a typical low light scene, the camera needs to capture light for a period of tens to hundreds of milliseconds. In such a situation (and assuming that the scene is static and the user/camera has correctly set the focus), the dominant contribution to the blur kernel is the camera shake—mostly due to hand tremors.
Current cameras including those found in camera phones are designed to take a burst of images. This has been exploited in several approaches for accumulating photons in the different images and then forming an image with less noise (mimicking a longer exposure time a posteriori. However, this principle is disturbed if the images in the burst are blurred. The classical mathematical formulation of this problem as a multi-image deconvolution, seeks to solve an inverse problem where the unknowns are the multiple blurring operators and the underlying sharp image. This procedure is computationally very expensive (prohibiting its on-camera implementation), and very sensitive to a good estimation of the blurring kernels. Furthermore, since the inverse problem is ill-posed it relies on priors either or both for the calculus of the blurs and the latent sharp image.